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Theorem heap-order-add-smaller
n + 1 ≤ # kar, n ≠ 0 ⊦ heap-order(kar, n) ∧ ¬ ki.key < kar[(n - 1) / 2].key → heap-order(kar[n, ki], n + 1)
Type: A user defined theorem
Validity: The proof is valid.
Features: ss, lss,
Comment:
Used by:
Used by units in proved state:
bin-min-heap-prepost
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 1
Proof steps: 14
Used lemmas:
heap-order
,
Used spec theorems:
Used simplifier rules:
nat
/
fle-01
nat-basic
/
succ
nat-basic
/
trans
nat-basic
/
lf
nat-div
/
two-ls-02
nat
/
succ-01
array
/key-index-array/
cngetput
nat-basic
/
zero-01
nat
/
elim-pred-c
nat
/
lels
nat-basic
/
s-04
key-index
/
elim
nat-basic
/
lf-02
array
/key-index-array/
Put-same
key-index
/
inj
nat
/
ler
oelem
/binheap-key/
lel
nat-basic
/
f
nat
/
lels-02
nat-basic
/
eq-01
array
/key-index-array/
Put-other
nat-basic
/
neq-04
nat-basic
/
ls-02
nat-basic
/
a
nat-basic
/
c
nat-basic
/
oz
nat
/
add-01
nat-basic
/
add-base
key-index
/
sel-02